GOFlaio2004              package:nsRFA              R Documentation

_G_o_o_d_n_e_s_s _o_f _f_i_t _t_e_s_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     Anderson-Darling goodness of fit tests for extreme-value
     distributions, from Laio (2004).

_U_s_a_g_e:

      A2_GOFlaio (x, dist="NORM")
      A2 (F)
      W2 (F)
      fw2 (w)

_A_r_g_u_m_e_n_t_s:

       x: data sample

    dist: distribution: normal '"NORM"', log-normal '"LN"', Gumbel
          '"GUMBEL"', Frechet '"EV2"', Generalized Extreme Value
          '"GEV"', Pearson type III '"P3"', log-Pearson type III
          '"LP3"'

       F: cumulative distribution function (that has to be sorted
          increasingly)

       w: Transformed test statistic (Laio, 2004)

_D_e_t_a_i_l_s:

     An introduction on the Anderson-Darling test is available on <URL:
     http://en.wikipedia.org/wiki/Anderson-Darling_test> and in the
     'GOFmontecarlo' help page. The original paper of Laio (2004) is
     available on his web site.

_V_a_l_u_e:

     'A2_GOFlaio' tests the goodness of fit of a distribution with the
     sample 'x'; it return the value A_2 of the Anderson-Darling
     statistics and its probability P(A2).  If P(A2) is, for example,
     greater than 0.90, the test is not passed at level alpha=10%.

     'A2' is the Anderson-Darling test statistic; it is used by
     'A2_GOFlaio'.

     'W2' is the Cramer-von Mises test statistic.

     'fw2' is the approximation of the probability distribution of 'w'
     (first 2 terms) when H_0 is true (Anderson-Darling, 1952); it is
     used by 'A2_GOFlaio'.

_N_o_t_e:

     For information on the package and the Author, and for all the
     references, see 'nsRFA'.

_S_e_e _A_l_s_o:

     'GOFmontecarlo', 'MLlaio2004'.

_E_x_a_m_p_l_e_s:

     sm <- rand.gumb(100, 0, 1)
     ml <- ML_estimation (sm, dist="GEV"); ml
     F.GEV(sm, ml[1], ml[2], ml[3])
     A2(sort(F.GEV(sm, ml[1], ml[2], ml[3])))
     A2_GOFlaio(sm, dist="GEV")

     ml <- ML_estimation (sm, dist="P3"); ml
     A2(sort(sort(F.gamma(sm, ml[1], ml[2], ml[3]))))
     A2_GOFlaio(sm, dist="P3")

